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Lai, Shaoyong

The local strong and weak solutions for a nonlinear dissipative Camassa-Holm equation. (English) Zbl 1228.35204

Abstr. Appl. Anal. 2011, Article ID 285040, 15 p. (2011).
Summary: Using the Kato theorem for abstract differential equations, the local well-posedness of the solution for a nonlinear dissipative Camassa-Holm equation is established in space \(C([0, T), H^s(R)) \cap C^1([0, T), H^{s-1}(R))\) with \(s > 3/2\). In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space \(H^s(R)\) with \(1 \leq s \leq 3/2\) is developed.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35D30 Weak solutions to PDEs

Keywords:

Camassa-Holm equation
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\textit{S. Lai}, Abstr. Appl. Anal. 2011, Article ID 285040, 15 p. (2011; Zbl 1228.35204)
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References:

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